Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
but also things like
human(Socrates ∧ Plato)
(human ∧ Greek)(Socrates)
((snub-nosed ∧ Greek)(human))(Socrates)
(((to ∧ from)(Athens))(walked))(Socrates)
• Standard logical inference is deep, uses few inference rules, and depends on few premises, while typical
human reasoning seems rather shallow, with possibly a large number of inference rules and multiple
supports for each premise. – We discuss this in §16.5.1 below.
• Standard logical inference seems well designed for monotonicity-based inferences, and negative-polarity
items of various kinds (any, ever, yet, a red cent, give a damn, one bit, budge an inch) provide a visible
syntactic reflex of this. For example:
i. every publisher of any book will get his money
ii. * every publisher of Plato will get any money
iii. no publisher of Plato will get any money
We see in these sentences that the contexts in which any can appear with this meaning depend on the
quantifier in some way. Roughly, any can appear only in monotone decreasing contexts – where this
notion is explained below, a notion that is relevant for a very powerful inference step. We will see that
“the second argument of every” is increasing, but “the second argument of no” isdecreasing.
12 Review: first semantic categories
12.1 Things
Let’s assume that we are talking about a certain domain, a certain collection of things. In a trivial case, we
might be discussing just John and Mary, and so our domain of things, or entities is:
E ={j,m}.
A simple idea is that names like John refer to elements of the universe, but Montague and Keenan and many
others have argued against this idea. So we will also reject that idea and assume that no linguistic expressions
refer directly to elements of E.
12.2 Properties of things
The denotations of unary predicates will be properties, which we will identify “extensionally,” as the sets of
things that have the properties. When E is the set above, there are only 4 different properties of things,
℘(E) ={∅, {j}, {m}, {j,m}}.
We can reveal some important relations among these by displaying them with with arcs indicating subset
relations among them as follows:
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